Install fan on gfci?

[EightFingers]

This is going in the kitchen. Before anyone says it’s a bad idea because of grease, etc., I should let you know the kitchen is huge, about 600 sqft so the fan will be far from the stove. 
Anyway I thought I’d use the 20 amp circuit that feeds two outlets on one of the countertops. These are fed by a gfci. There are a lot of wires in the box that houses the gfci, so I thought I’d put one of the outlets and the fan switch in a new two gang box and go from there. Wiring would be much simpler that way. 
Is this doable?

[MstrCarpenter]

That would work. If it's a GFCI receptacle (vs. a breaker in your panel) you could wire it to the load side for the added protection to the fan. Most 15a GFCI receptacles protect 20a wired on the load side.

[EightFingers]

Thanks.

When I googled that, there was no direct answer. What I saw mostly was people having problems with “old” fans and others saying the gfci was tripped when the fan was turned off. The theory being the fan turned into a “generator” as it spun down sending a current into the gfci tripping it.